Question

cool down: circular logic
conjecture: any 2 circles in the plane are congruent.
do you agree or disagree with the conjecture? if you agree, explain how you know. if you disagree, edit the conjecture so it will always be true.

Explanation:

Two circles are congruent if and only if they have the same radius. Since circles in a plane can have different radii, the original conjecture is false. To make it true, we can change it to a statement about similar circles. All circles are similar because the ratio of the circumferences of any two circles is equal to the ratio of their radii.

Answer:

Disagree. Edited conjecture: Any 2 circles in the plane are similar.